It All Adds Up - Just the Facts, Ma'am?

There’s an old quote that goes “If the law is against you, argue the facts. If the facts are against you, argue the law. If both are against you, pound the table and yell like hell!” It’s a nice line, but it’s the first two sentences that carry the real message: sometimes facts are completely irrelevant.

That might sound like a stupid thing to say. It might sound more stupid still coming from someone who makes their living acquiring huge sets of numbers and trying to tease out the underlying truths they reveal.

What the above quotation is really saying, though, and what I want to get at, is this: some facts are more important than others.

It doesn’t take much knowledge of our legal system (or many others) to know that occasionally you can be perfectly sure that the defendant has deliberately killed another human being, but be equally aware that they will never be found guilty of murder. Perhaps the legal definition of murder doesn’t encompass exactly what they did - if it was clearly in self-defence, for example, or in the defence of others. Perhaps there is sufficient evidence of malpractice by the state that the law demands the defendant be released*. Either way, there are times where you could have, to quote Blackadder, a signed confession saying “I’m glad I killed the bastard”, and it wouldn’t make any difference. The immutable facts embedded in our legal mechanisms trump the paltry knowledge that someone deliberately killed someone else.

A similar situation exists in mathematics. The legal system has its rules; we have ours. In both cases, it comes down to application of the logic. Logic and facts are concepts which orbit around a central point, with each powering and complementing the other. Use either badly, and the other suffers. Logic applied in denial of prudent facts leads to ridiculous conclusions, but an obsession with facts (and one man’s fact is another man’s factoid) without logical appraisal leads to blind alleys and hypocrisies, and ultimately fanaticisms.

I came across a minor but fairly telling reminder of all this a few years ago, when I entered a long discussion about whether Marvel’s temporary killing of Captain America and DC’s similar move with Batman was suggestive of plagiarism. The unofficial prosecution in our impromptu trial hoped to prove their case with a laundry list of similarities between the two stories.

To me, those lists were profoundly inconclusive (like saying Quantum Leap rips off Doctor Who because both series make a mockery of linear time), and I said so, offering my arguments as to why the similarities could easily be considered coincidence.

The thing is; I’ve never read either story. For all I know, Marvel spent ten minutes photo-shopping Steve Rogers over the top of Bruce Wayne and then hit “PRINT”.** Establishing the fact of whether or not plagiarism occurred was something I couldn’t speak to. All I could argue was that the evidence offered was woefully short of convincing.

Long story short, this did not impress the prosecution. How could I possibly comment on the plagiarism accusation, they demanded, if I hadn’t actually compared the two stories? Without even knowing who was being accused of copying whom?

There is a subtle but vitally important point buried in all of this. My intentions had been entirely misunderstood. My argument was never that no plagiarism was involved. It was quite simply that their evidence did not logically imply plagiarism.

Statisticians, as I’ve said, operate a lot like lawyers. It’s not that we don’t care what really happened - far from it - it’s simply that from our perspective, the evidence assembled either proves a case, or it doesn’t.

I was reminded of all this a few days ago, when the case against Dominique Strauss-Kahn collapsed. For those who haven’t been following this story, Mr Strauss-Kahn (henceforth called DSK, because I’m running out of wick) – at that time the Managing Director of the International Monetary Fund (IMF) - was accused in May of raping a hotel maid in New York, and was arrested before his plane could leave the runway.

Initially, the case against him seemed reasonably strong. There was certainly evidence that he and the maid had engaged in sexual acts, the maid had both bruises and no criminal record, and the novelist Tristane Baton quickly claimed that DSK had tried something similar with her years before. That, pretty much, was the full extent of what anyone outside of the US legal system had to go on.

Almost immediately, the Internet went crazy.*** Blog posts and op-ed pages sprang up everywhere, filled with pointless, uninformed speculation. Some people praised hotel staff, and others lambasted them, as though everyone who makes money cleaning rooms behaves in the same way. Friends of DSK spent gallons of ink telling us they didn’t believe he could possibly be guilty, forgetting that the maid in question lacked influential friends to make similar cases on her behalf. Several very influential people, who really ought to have known better, expressed their disgust over a legal system that would arrest someone like DSK simply because an immigrant hotel maid alleged rape (exactly how many immigrant maids would need to accuse DSK of sexual assault before his noble wrists should be sullied with handcuffs was left unstated).

In response, a lot of people - including me, in my last article – attempted a little pushback. We did so fully aware that we had no idea whether the rape charge was true or not. We weren’t arguing that DSK was guilty, any more than I was arguing two years ago that the Captain America/Batman stories were created entirely independently. We were just pointing out that the arguments in favour of DSK’s innocence were completely, demonstrably ridiculous.

One of the hardest truths of the internet is that sometimes even the most worthless non-thinker can hit upon the truth by accident. It now seems that the maid has been caught lying to the police. Not about the rape itself, perhaps, but many other things, from the events of that day to the way she originally entered the US, meaning that her credibility on pretty much any issue has now been severely compromised.

So, the DA is liable to drop the case, and he’s doing it to the sound of dozens of thoroughly unlikeable people crowing that this “proves” he should never have listened to the maid in the first place.

That kind of argument drives me mad. An uninformed, unthinking, pro-wealth, anti-immigrant, anti-woman (delete as applicable) position is not vindicated when its entirely unsupportable assertions actually prove to be true. If I toss a coin and announce that anyone who thinks it will come down tails is an idiot, watching the coin land heads up is not proof that I was right.

DSK has been freed not because we now know there was no rape, but because legal realities take precedence: there is almost no chance of conviction. The buried fact of whether the rape took place has been rendered irrelevant by something more immediate – a case with one witness cannot survive that witness proving untruthful.

The people who argued that maids can’t be trusted have not been proved right, merely not invariably wrong. Everyone who criticised the United States because they will arrest someone when there is credible evidence they are a rapist even if they’re the head of the IMF has not been vindicated, because - and this cannot possibly be stressed enough - whether the decision to arrest someone was right or not does not depend on whether or not they are later found to be guilty. There’s a horribly ugly subtext to all of this “I told you so!” finger-wagging, and that’s the idea that next time a poor woman accuses a rich man of having raped her, we’d better think twice before we believe her.

This, though, is where statisticians - and lawyers - tend to diverge from so much of the modern media, and the people to whom they offer a microphone. To us, a lack of evidence means nothing can be said. To them, a lack of evidence means everything must be assumed.

* My father, a solicitor, summed up the OJ trial as follows: “There’s no way anyone should be convicted when the system accusing them has proven itself to be this incompetent and racist. Mind you, I’m quite convinced he did it.”

** Assuming that’s even the right way round. I still have no idea. And don’t come whining to me about a lack of research: the power is out in my flat and I’m writing this on my laptop by candlelight. Because I care.

*** The conservative American press seemed particularly confused, because they were being asked how one should treat a successful high-society businessman who was also a French socialist.